GLOBAL WEAK SOLUTIONS OF 3D COMPRESSIBLE MICROPOLAR FLUIDS WITH DISCONTINUOUS INITIAL DATA AND VACUUM
GLOBAL WEAK SOLUTIONS OF 3D COMPRESSIBLE MICROPOLAR FLUIDS WITH DISCONTINUOUS INITIAL DATA AND VACUUM
复制标题
具有不连续初始数据和真空的 3d 可压缩微极性流体的全局弱解
DOI：
10.4310/cms.2015.v13.n1.a11
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发表时间：
2015-01-01
影响因子：
1
通讯作者：
Zhang, Jianwen
中科院分区：
文献类型：
--
作者：
Chen, Mingtao;Xu, Xinying;Zhang, Jianwen
本文研究了具有间断初值的三维可压缩微极流体方程柯西问题弱解的整体存在性。这里假定L-2的初始能量较小，初始密度在L无穷大内有界，L-2的初始速度和微转动速度的梯度有界。具体地说，这意味着初始数据可能包含真空态，并且解的振荡可能任意大。作为副产品，我们还证明了具有严格正密度和小初始能量的整体光滑解的存在性。
In this paper, we study the global existence of weak solutions to the Cauchy problem for three-dimensional equations of compressible micropolar fluids with discontinuous initial data. Here it is assumed that the initial energy is suitably small in L-2, that the initial density is bounded in L-infinity, and the gradients of initial velocity and microrotational velocity are bounded in L-2. Particularly, this implies that the initial data may contain vacuum states and the oscillations of solutions could be arbitrarily large. As a by product, we also prove the global existence of smooth solutions with strictly positive density and small initial-energy.